diff --git a/internal/ceres/graph_algorithms.h b/internal/ceres/graph_algorithms.h
index b1c42c6..cb9913a 100644
--- a/internal/ceres/graph_algorithms.h
+++ b/internal/ceres/graph_algorithms.h
@@ -49,6 +49,9 @@
       : graph_(graph) {}
 
   bool operator()(const Vertex& lhs, const Vertex& rhs) const {
+    if (graph_.Neighbors(lhs).size() == graph_.Neighbors(rhs).size()) {
+      return lhs->user_state() < rhs->user_state();
+    }
     return (graph_.Neighbors(lhs).size() < graph_.Neighbors(rhs).size());
   }